back court question
 

is a backcourt if your feet are in the frontcourt and the ball is being dribbled on the division line

Depends on the scenario...

If a player is dribbling a ball from the backcourt, then the ball is not considered in the frontcourt until the ball and both feet of the dribbler are in the frontcourt. In this case, a player could dribble the ball with both feet in the frontcourt and the ball touching the division line (the whole line is considered part of the backcourt).

Now if you're imagining the scenario where the ball is already in the frontcourt during normal play, and a player catches the ball near the halfcourt line, then dribble the ball on the line with both feet in the frontcourt, then you would have a backcourt violation.

If you could give us a better hypothetical scenario with more information, then we could more fully answer your question.

To Be Specific ...
 

... which would occur when the dribbled ball touches the backcourt (which includes the division line) and then touches the hand of the dribbler, or any offensive player, after the "bounce" in the backcourt.

back court
 

:)

Don't forget that in this case, the 10 second backcourt count would continue.